As you know Argonia separated from the empire and is now called the An-Xileel.First question is what exactly is the An-Xileel? are they a political party or is Argonia simply now called An-Xileel. Secound question, is Morrowind officially conquered by the Argonians ? or was it simply occupied for a short time?

Argonia isn't called An-Xileel; it's still interchangeably referred to as Argonia and Black Marsh. The An-Xileel are a political party that came to dominate the region at the beginning of the Fourth Era. The Saxhleel war effort was primarily concentrated in the southern parts of Morrowind (especially the areas that used to belong to Argonians), and much of Morrowind was probably never even touched by the invasion. These parts were still sort of occupied as of 4E40, but the Saxhleel weren't really doing much with the territory.